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Math  /  Algebra

Question29. The rocket sled shown below decelerates at a rate of 196 m/s2196 \mathrm{~m} / \mathrm{s}^{2}. What force is necessary to produce this deceleration? Assume that the rockets are off. The mass of the system is 2.10×103 kg2.10 \times 10^{3} \mathrm{~kg}.

Studdy Solution

STEP 1

1. The rocket sled is decelerating at a rate of 196 m/s2196 \, \mathrm{m/s}^2.
2. The mass of the system is 2.10×103 kg2.10 \times 10^3 \, \mathrm{kg}.
3. The rockets are off, so the only force acting is the decelerating force.
4. We are trying to find the force necessary to produce this deceleration.

STEP 2

1. Identify the relevant physics principle.
2. Write the formula for force.
3. Substitute the given values into the formula.
4. Calculate the force.

STEP 3

Identify the relevant physics principle.
The relevant principle here is Newton's second law of motion, which states that force is the product of mass and acceleration.

STEP 4

Write the formula for force.
According to Newton's second law, the force F F can be calculated using the formula:
F=m⋅a F = m \cdot a
where m m is the mass and a a is the acceleration (or deceleration in this case).

STEP 5

Substitute the given values into the formula.
Given: - Mass m=2.10×103 kg m = 2.10 \times 10^3 \, \mathrm{kg} - Deceleration a=196 m/s2 a = 196 \, \mathrm{m/s}^2
Substitute these values into the formula:
F=(2.10×103 kg)⋅(196 m/s2) F = (2.10 \times 10^3 \, \mathrm{kg}) \cdot (196 \, \mathrm{m/s}^2)

STEP 6

Calculate the force.
Perform the multiplication:
F=2.10×103×196 F = 2.10 \times 10^3 \times 196
F=411600 N F = 411600 \, \mathrm{N}
The force necessary to produce this deceleration is:
411600 N \boxed{411600 \, \mathrm{N}}

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